Evidence against the simulation hypothesis

1. Evidence Against the
Simulation Hypothesis
© Peter Morgan Oct 2017 1
Peter Morgan

2. What Is the Simulation Hypothesis?
 The Simulation Hypothesis (SH) is the speculation that the observable
universe is a simulation created by a superior being, much in the same
way that we currently produce realistic 3D video games or environments
 It is not a new theory - it recently gained attention by Elon Musk saying
on National TV that he’s pretty sure we are living in a simulation [1]
 Essentially we can assign a probability of the SH being correct between 0
and 1. 0 means that the universe is absolutely certainly not a simulation,
and 1 means that the universe is a simulation with 100% certainty
 So 0 < P[SH is true] < 1
 Different people assign different values to the simulation hypothesis
being true [2]
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3. Arguments For & Against
 People who believe that the SH may be true argue that it is likely
because, just as we create video games, so we can extrapolate to a time
in the future whereby, with enough compute power, we could simulate
our entire universe
 To disprove the SH we (scientists) have to show why this cannot happen
 The laws of physics, including computation and energy conservation, are a
good place to start [3], [4]
 We will need to understand what computation and information processing
entail
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4. The Scientific Method – Appeal to Reason
 It’s easy to say something is possible, harder to do the physics (aka anybody
can say anything, but this certainly does not make it true)
 Note on the scientific method – a hypothesis is as powerful as the testable
predictions that it makes
 You can never prove a theory right, only disprove it
 What we can do, however, is to show that something is so unlikely that it is
effectively impossible, and that other theories are therefore, much more
likely to be correct
 For example, the big bang theory of creation is currently much more likely to
be the correct theory of creation than the simulation hypothesis
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5. What is Needed Computationally
 To disprove the SH, we need to show that it is physically impossible (or
exceedingly unlikely) to create a universe such as ours by
computational means
 What would it take to recreate our universe down to the scale
(granularity) currently measured by particle accelerators, or smaller?
d < 10TeV ~ 10^-19m
 And up to the large scale structure of our universe (approx. 46 billion
light-years, or 5 x 10^23km)
 Not to mention the creation of sentient beings (us) who can think
intelligently about such a hypothesis.
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6. Computation in the Biosphere
 There are approximately 10^80 atoms in the universe. Many of these are arranged
into very complex organic systems, or living organisms. These include humans,
animals, plants, fungi, bacteria and viruses
 We can estimate how many of these atoms are involved in living organisms. And
then calculate the processing power required to simulate all life in our biosphere
 In humans, there are approximately 10 trillion cells. Multiply this by the number of
humans on Earth (10 billion, order of magnitude)
 There are approximately 10 million species in all five classes of life [5]
 Estimate that on average there are 10 billion cells in each of these species (I have
taken 0.1% of the number of cells in a human)
 We then have 10^13 x 10^10 x 10^7 x 10^10 = 10^40 cells total for all the life on
Earth (in the biosphere)
 Another way at getting at this is by estimating the number of atoms in an average
adult human which is around 10^28 [6], but here we will follow the cellular
approach.
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7. Computation in the Biosphere
 How much compute power (TFlops, memory) is needed to simulate the 10^40
cells involved in life on Earth? We can get an idea by estimating the total DNA in
the Earth’s biosphere. From [7]:
 "Finding the amount of DNA in the biosphere enables an estimate of the
computational speed of the biosphere, in terms of the number of bases
transcribed per second, or Nucleotide Operations Per Second (NOPS), analogous
to the Floating-point Operations Per Second (FLOPS) metric used in electronic
computing
 If all the DNA in the biosphere was being transcribed at these reported rates,
taking an estimated transcription rate of 30 bases per second, then the
potential computational power of the biosphere would be approximately 10^24
PetaNOPS
 This is about 10^22 times more processing power than the Tianhe-2
supercomputer [8], which has a processing power on the order of 100
PetaFLOPS."
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8. Computation in the Biosphere
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Figure 1 – DNA Computation Equivalence

9. Space and Power Requirements
 How much space would 10^22 Tianhe-2's take up? Let's say that a Tianhe-2
supercomputer takes up an area of 100m^2
 We would then need 10^24m^2 of space
 The surface area of the Earth is 5 x 10^14m^2, so we would need the
surface area of 10 billion Earths just to calculate the DNA computations on
Earth given the current state of HPC
 How much power would we need? Let's say that Tianhe-2 uses 25MWh. We
would then need 10^22 x 2.5 x 10^7 MWh = 2.5 x 10^17 TWh of power
 The current electricity generation capacity of Earth is around 2.5 x 10^16
TWh [9], so we would need 10X the entire Earths' electricity generation
capacity given current HPC energy performance
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10. Life on Other Planets
 The above calculations are just for life here on Earth. What if there is life
elsewhere in the universe, which recent Exoplanet observations indicate the
potential for?
 Let's say there are 1 billion planets with life in the Milky Way and that, on
average, they contain a similar amount of life in their biospheres as Earth
 We need to multiply 10^40 by 10^9 x 10^11 (there are 100 billion galaxies in
the observable universe) to give us a figure of 10^60 cells in the universe
 This is 10^20 times more computation than was needed in the calculations
for life on Earth alone
 It is hard for us to imagine another universe existing with the computational
resources (hardware, energy) required to make such an elaborate simulation
of this universe
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11. High Energy Cosmic Rays
 Paper by physicists at the University of Washington examining the limits to the
SH [10]
 Observable consequences of the hypothesis that the observed universe is a
numerical simulation performed on a cubic space-time lattice or grid are
explored
 Assumption: simulations of the future employ an underlying cubic lattice
structure
 Are there any signatures of a simulated universe that might be experimentally
detectable?
 One proposed signature is in the anisotropy of high energy cosmic rays (Note –
the GZK limit is the theoretical upper limit on the energy of cosmic rays)
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12. Conclusions
 The above calculations are just for DNA replications of all
organisms. There are other processes and interactions occurring
here on Earth and in the universe, that would require further
orders of magnitude more computational resource
 No evidence whatsoever from experimental probes so far
 In conclusion, the SH is extremely unlikely to be correct
 In principle there always remains the possibility for the
simulated to discover the simulators
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13. References
 [1] Elon Musk believes we are probably characters in some advanced
civilization's video game
http://www.vox.com/2016/6/2/11837608/elon-musk-simulation-argument
 [2] Are You Living In a Computer Simulation?
http://www.simulation-argument.com/
 [3] Lloyd, Seth, Ultimate Physical Limits to Computation, Nature, 406,1047,
1999 https://arxiv.org/abs/quant-ph/9908043
 [4] Wolfram, Stephen, A New Kind of Science, Wolfram Media, 2002
 [5] How many species are there on Earth?
https://www.sciencedaily.com/rel.../2011/08/110823180459.htm
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14. References
 [6] How many atoms are in the human body?
https://education.jlab.org/qa/mathatom_04.html
 [7] Landenmark et al, An estimate of the total DNA in the biosphere,
PLOS Biology, 2015
http://journals.plos.org/plosbiology/article?id=10.1371%2Fjournal.pbi
o.1002168
 [8] Tianhe-2 https://en.wikipedia.org/wiki/Tianhe-2
 [9] BP Energy Review 2016
https://www.bp.com/.../statistical.../electricity.html
 [10] Beane et al, Constraints on the Universe as a Numerical
Simulation, 2012 https://arxiv.org/abs/1210.1847v2
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